Two metal wires of identical dimensions are connected in series. If σ1 and σ2  are the conductivities of the metal wires respectively, the effective conductivity of the combination is

As both metal wires are of identical dimensions, so their length and area of cross-section will be same. Let them be I and A respectively. Then The resistance of the first wire isR1=lσ1A                                ....(i)and that of the second wire is R2=lσ2A                       ...(ii)As they are connected in series, so their effective resistance isRs=R1+R2=lσ1A+lσ2A  ( using (i) and  (ii))=lA1σ1+1σ2                  . . .(iii)If σeff is the effective conductivity of the combination, thenRs=2lσeff A                        . . . .(iv)Equating eqns. (iii) and (iv), we get 2lσeffA=lA1σ1+1σ22σeff =σ2+σ1σ1σ2⇒σeff =2σ1σ2σ1+σ2